The last step is to make the connection between the Landau singularities found in this way and the vanishing of symbol letters; and specifically to test the expectation that the heptagon symbol alphabet captures the singularities of all seven-point amplitudes in SYM theory. The 49 symbol letters of the heptagon alphabet (see [1]}, [2]}) fall into seven classes under the \(Z_i \rightarrow Z_{i+1}\)  cyclic group. Let us denote the letters by
\(b_{01}=\mathinner {\langle {1234}\rangle },\qquad b_{11}=\mathinner {\langle {1256}\rangle },\qquad b_{21}=\mathinner {\langle {1456}\rangle },\qquad b_{31}=\mathinner {\langle {1236}\rangle },\\b_{41}=\mathinner {\langle {1346}\rangle },\qquad b_{51}=\mathinner {\langle {1(23)(45)(67)}\rangle },\qquad b_{61}=\mathinner {\langle {1(34)(56)(72)}\rangle },\) 
